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user100 [1]
3 years ago
14

Natalie is skiing along a circular ski trail that has a radius of 2.6 km. She starts at the 3-o'clock position and travels in th

e CCW direction. Natalie stops skiing when she is 0.942 km to the right and 2.423 km above the center of the ski trail. Imagine an angle with its vertex at the center of the circular ski trail that subtends Natalie's path.
a. How many radians has the angle swept out since Natalie started skiing? ______radians
b. How many km has Natalie skied since she started skiing? _________km

Mathematics
1 answer:
N76 [4]3 years ago
6 0

Answer:

  • 1.20 radians
  • 3.12 km

Step-by-step explanation:

a. The tangent of the central angle is the ratio ...

  tan(θ) = (2.423 km)/(0.942 km) . . . . . definition of tangent

  θ = arctan(2.423/.942) ≈ 1.200 radians

__

b. The length of the arc is ...

  s = rθ = (2.6 km)(1.2 radians) = 3.12 km

_____

The attached output from a graphics program shows the angle as 68.76°. Multiplying by π/180°, we can convert that to radians:

  θ = 68.76π/180 = 216.0/180 = 1.200 radians

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A triangle is removed from the rectangle. Find the area of the remaining figure.
Mariulka [41]

Answer

C) 160 in^2


Step by step explanation

First, let's find the area of the rectangle.

Area of a rectangle = length x width

The area of the rectangle = 20 * 10

= 200 in^2

Now let's find the area of the triangle that is removed.

Area of a triangle = 1/2 base * height.

Here base = 10 and height = 8. Plug in these values into the formula, we get

Area of the triangle = 1/2 * 10*8

= 5* 8

The area of the triangle = 40 in^2

The area of the remaining figure = Area of the rectangle - area of the triangle

=  200 - 40

= 160 in^2

The answer is "160 in^2"

Thank you.

5 0
3 years ago
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inn [45]

Answer:

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Step-by-step explanation:

Given

A = \frac{1}{2} bh

Multiply both sides by 2 to clear the fraction

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4 0
3 years ago
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natta225 [31]

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Step-by-step explanation:

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1 year ago
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Step-by-step explanation:

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Answer:

b)

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Step-by-step explanation:

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